In the design stage of producing goods, design conditions are expressed as a function (in other words, an objective function) of predetermined design parameters, and design parameters are set so that the value of the objective function becomes, for example, minimum. At that time, after the designer determines the basic shape, the designer sets the allowable range of fluctuation for each design parameter and performs optimization within the design parameter space. However, when attempting to search the entire design parameter space in the case of a large number of design parameters, an explosion of combinations occur resulting in an enormous number of combinations, thus making calculation impossible in real time.
There are a large number of techniques to carry out such optimization processing at high speed by the numeral calculation.
On the other hand, in an optimization design by computer simulation, there is a method called optimization by computer algebra. In such a method, computer simulation is performed for the values of various design parameters, and output evaluation indicators are calculated for each individual case. Then, model expressions that approximate the relationships between the design parameters and output evaluation indicators are calculated, and optimization by the computer algebra is carried out based on these model expressions. As a processing for the optimization, expressions that represent the relationship between cost and performance are calculated from the obtained approximate expressions and constraints.
Incidentally, as for the computer algebra, a Quantifier Elimination (QE) method is known. This technique is a technique that an expression “∃x (x2+bx+c=0)”, for example, is changed to an equivalent expression “b2−4c≧0” by eliminating quantifiers such as “∃ and ∀”.
Specifically, the QE method is described in the following document. However, because a lot of documents for the QE method exist, useful documents other than the following document exist. This document is incorporated herein by reference.
Jirstrand Mats, “Cylindrical Algebraic Decomposition—an Introduction”, Oct. 18, 1995.
However, there is a problem that the amount of calculation is large even using QE. Therefore, it becomes necessary to simplify the problem by reducing the number of constraints, or to simplify the model by decreasing the order of the model expression, or reducing the number of variables and terms. However, such a kind of simplification increases error. Therefore, the influence is large, when searching for one point that provides the optimum solution.
Namely, the conventional arts cannot carry out the optimization processing solving the aforementioned problem at high speed by the computer algebra.